This paper studies subsampling hypothesis tests for panel data that may be nonstationary, cross-sectionally correlated, and cross-sectionally cointegrated. The subsampling approach provides approximations to the finite sample distributions of the tests without estimating nuisance parameters. The tests include panel unit root and cointegration tests as special cases. The number of cross-sectional units is assumed to be finite and that of time-series observations infinite. It is shown that subsampling provides asymptotic distributions that are equivalent to the asymptotic distributions of the panel tests. In addition, the tests using critical values from subsampling are shown to be consistent. The subsampling methods are applied to panel unit root tests. The panel unit root tests considered are Levin, Lin, and Chu's (2002) t-test; Im, Pesaran, and Shin's (2003) averaged t-test; and Choi's (2001) inverse normal test. Simulation results regarding the subsampling panel unit root tests and some existing unit root tests for cross-sectionally correlated panels are reported. In using the subsampling approach to examine the real exchange rates of the G7 countries and a group of 26 OECD countries, we find only mixed support for the purchasing power parity (PPP) hypothesis. We then examine a panel of 17 developed stock market indexes, and also find only mixed empirical support for them exhibiting relative mean reversion with respect to the US stock market index.